Ab initio interaction potential of methane and nitrogen

On the determination of Lennard-Jones parameters for polyatomic molecules

Characterizing the key length and energy scales of intermolecular interactions, Lennard-Jones parameters, i.e., collision diameter and well depth, are prerequisites for predicting transport properties and rate constants of chemical species in dilute gases. Due to anisotropy in molecular structures, Lennard-Jones parameters of many polyatomic molecules are only empirically estimated or even undetermined. This study focuses on determining the effective Lennard-Jones parameters between a polyatomic molecule and a bath gas molecule from interatomic interactions. An iterative search algorithm is developed to find orientation-dependent collision diameters and well depths on intermolecular potential energy surfaces. An orientation-averaging rule based on characteristic variables is proposed to derive the effective parameters. Cross-interaction parameters for twelve hydrocarbons with varying molecular shapes, including long-chain and planar ones, interacting with four bath gases He, Ar, N₂, and O₂ are predicted and reported. Three-dimensional parametric surfaces are constructed to quantitatively depict molecular anisotropy. Algorithmic complexity analysis and numerical experiments demonstrate that the iterative search algorithm is robust and efficient. By using the latest experimental diffusion data, it is found that the proposed orientation-averaging rule improves the prediction of cross-interaction Lennard-Jones parameters for polyatomic molecules, including for long-chain molecules that challenge the consistency of previous methods. By introducing characteristic variables, the present study shows a new route to determining effective Lennard-Jones parameters for polyatomic molecules.

Fitting potential energy and induced dipole surfaces of the van der Waals complex CH4-N2 using non-product quadrature grids

We present an extensive study of the five-dimensional potential energy and induced dipole surfaces of the CH₄-N₂ complex assuming rigid-rotor approximation. Within the supermolecular approach, ab initio calculations of the interaction energies and dipoles were carried out at the CCSD(T)-F12 and CCSD(T) levels of theory using the correlation-consistent aug-cc-pVTZ basis set, respectively. Both potential energy and induced dipole surfaces inherit the symmetry of the molecular system and transform under the A₁⁺ and A₂⁺ irreducible representations of the molecular symmetry group G₄₈, respectively. One can take advantage of the symmetry when fitting the surfaces; first, when constructing angular basis functions and second, when selecting the grid points. The approach to the construction of scalar and vectorial basis functions exploiting the eigenfunction method [Q. Chen, J. Ping and F. Wang, Group Representation Theory for Physicists, World Scientific, 2nd edn, 2002] is developed. We explore the use of Sobolev-type quadrature grids as building blocks of robust quadrature rules adapted to the symmetry of the molecular system. Temperature variations of the cross second virial coefficient and first classical spectral moments of the rototranslational collision-induced band were derived. A reasonable agreement between calculated values and experimental data was found attesting to the high quality of constructed surfaces.

Molecular Collision Diameters and Electronic Polarizabilities: Inherent Relationship and Fast Evaluation

The collision diameter σ for a large set of molecular species is related to the static electronic polarizability α_el. A remarkable correlation between these quantities conceptually similar to the analogous one previously identified for atoms is revealed. Our recommended model is the function σ(α_el) = p₁ + p₂α_el^1/3, where p₁ = 0.768 Å and p₂ = 2.168 are the fitting parameters providing the best overall match to the reference data for collision diameter (181 data points). The obtained correlation allows one to easily find the collision diameter of molecules from the known polarizability and vice versa. These findings can be useful for many applications, where there is a need for inexpensive assessments of the collision diameters or electronic polarizabilities, for example, when developing the transport property databases for modeling of chemically reacting flows.